An end to The Killing: Soren Sveistrup reveals why Sarah Lund's third series will be her last

Twenty minutes north of Copenhagen by taxi, on a windswept business park near the intersection of two motorways, I find myself traipsing around the outside of a single- storey, glass-fronted block that supposedly houses the studios where The Killing is filmed.

None of the locals I asked for directions appeared to know that they have this internationally acclaimed dream factory in their midst, but when I do finally locate the premises but fail to find an unlocked entrance, I nose, Sarah Lund-like, through the windows. Let the imagination run riot and it could be a murder scene – or the morning after the night before (a few paper wine cups and party plates are strewn around). Certainly there's a distinct air of abandonment.

"It's a bit of a ghost town now," agrees Soren Sveistrup when I finally find a way in. "You should have seen it a few weeks ago… you couldn't move for people."

Sveistrup is creator of Denmark's biggest export since Carlsberg , Hans Christian Andersen and the Vikings – an ambitious TV police drama that has swept the globe, and given knitters of Faroese jumpers their biggest sales fillip since their 1970s heyday. From Brazil to South Korea, Canada to Australia, The Killing has won plaudits and devoted audiences. And of course, two years ago (three years after it was made), the subtitled saga, in which Copenhagen policewoman Sarah Lund investigated just one single murder over 20 hour-long episodes, plopped unceremoniously into BBC4's Saturday-night schedules, before becoming a word-of-mouth hit with the sort of speed that a bush fire might envy.

And this is where it all happens. Or, rather, happened. The final instalment, The Killing III, wrapped a month ago, and now Sveistrup labours almost alone in this soon-to-be mausoleum of his greatest hit as he completes the music and sound-editing. Is he sad that it's all nearly over, I ask as he gives me the guided tour of the set – Lund's office, the police interrogation room and so on. (Fittingly the lights don't seem to work, so we stroll through the scenery in semi-darkness.)

"It's a great relief right now," he says, "but think that around Christmas I'll be weeping. But then it was my own decision to do only three stories. I can do hundreds of episodes with Sarah Lund, but I don't think they'd be good ones. I watch a lot of British shows and US shows and they just go and on and on."

Sveistrup is a tall, slim man in his mid-forties, but his casual attire (black combat trousers and lumberjack shirt) make him seem younger. Although perfectly friendly and talkative, he gives hardly any interviews. "I'm not that much of a public type," he says, leading me into his inner sanctum, where he conducts meetings and works out plot development on whiteboards. It could almost be the nerve centre of a police murder inquiry, or a university seminar room, although Sveistrup prefers to liken his role of show-runner overseeing every aspect of The Killing, from original story idea to final edit, to that of a conductor. "I look at it as one big orchestra and I have to make sure the violin is playing the same tune as the drum."

So, cue a drum roll. The Killing III begins as usual with a single murder – here that of a sailor in Copenhagen's port – the ripples from which will lead Lund (played again by Danish actress Sofie Grabol) to a billionaire businessman and an embattled prime minister attempting to shore up a coalition alliance. "It's all about challenging Lund," says Sveistrup. "I remember at some point we had a lot of trouble with biker gangs in Denmark and people said to me, 'OK, those can be her new opponents,' but for me they're not big enough. Politically this is the final step because we started out [in series one] in city hall and then we had the minister of justice in the second series and now we have the prime minister. And this time we have other opponents in the financial sector."

Indeed, while child abduction is one of the motors of the new story, it is the ongoing economic crisis that provides the central theme. "Every time we turn on our television in Denmark it's something about the financial crisis," he says. "I don't know anything about money or stocks or anything, but I know something about emotions and I think that one of the themes in the financial crisis is that everybody's just taking care of themselves.

"All my ideas start with a feeling," he adds, "some sort of emotion – being sad that someone has died, a family getting disrupted or something like that. Afterwards I try to make it bigger – to bring in society. I'm telling you this because a reporter asked me about this because he'd just spoken to a Swedish writer [the Wallander author, Henning Mankell, it transpires], who said that everything begins with society. That's too schematic for me – I, too, want to examine something in society, but it starts with an emotion, otherwise I don't see the point."

Sveistrup was born in Copenhagen in 1968 and adopted as a baby, going to live with his new parents on the remote island of Thuro (population: 3,500) in the south of Denmark, returning to the capital to study history and literature at university. In his final year, he sent an application to study scriptwriting at the national film school. "It was an epiphany," he says. "You can use all your luggage, your feelings, to do something. It was a great liberation."

What was less liberating was the reality of obtaining finance for his epic cinematic vision. "When I finished film school in 1996, I thought, 'Now I'm going to write big films and send scripts to get production money.' And nothing happened. Danish Broadcasting had their eye on me and said, 'Why don't you come and work for us?' and I said, 'I don't have the time. I have to do my big work…' Actually, then I did some episodes for Danish television shows and nothing happened with these big movies and suddenly I realised there are people here who have confidence in me. Why don't I take the invitation? They gave me carte blanche to do whatever I wanted, so I said, 'OK, let's do cinema… something great.'"

However, a police show wasn't originally the Danish state broadcaster's idea of "something great". "You try to tell them it's not really a police story, it's something else – it's about destiny – and finally they bought it."

It, of course, was the first series of The Killing, or Forbrydelsen (literal translation, "The Crime"), as it's known locally. Sveistrup had already directed Grabol, a seasoned actress, in the relationship drama Nikolaj og Julie, a sort of Danish Cold Feet, five years earlier – winning an international Emmy in the process. Not everyone, however, was convinced that Grabol – known more for her emotional roles – was good casting as the driven, somewhat antisocial detective at the centre of The Killing.

"There was some talk of her not being right for the part," admits Sveistrup. "Sofie never did anything sinister at the time, she was very into comedy, she's very likeable. But she wanted something else; she was tired of playing the good-looking girl, and it was her idea to use the sweater to extract the whole sexuality from the character – hiding everything."

Lund's iconic sweater was originally going to have been a poncho, as worn by Clint Eastwood in his Spaghetti Westerns, but Grabol had problems drawing her gun while wearing a poncho. Then there was the famous incident when Sveistrup attempted to give Lund a romance with one of the suspects in the original Killing series and Grabol stormed into his office to protest that, "I am Clint Eastwood… he doesn't have a girlfriend."

But now is the first time that Sveistrup explicitly states that Lund was directly based on the Hollywood legend. "I've always been fond of Clint Eastwood," he says. "The parts he plays are so silent, sometimes a bit biblical. If you watch Dirty Harry he's not especially likeable and I like that paradox about a character. At the time the whole picture of female detectives was so disappointing – high-heeled detectives with a lot of mascara looking good, model types, dating the guy from forensics during the investigation… you just couldn't believe in it."

Sveistrup and Grabol's working relationship is unusually close – she would telephone him late at night to discuss points in the following day's shooting script, for example – although he says that since the birth of his two children, Grabol now texts rather than disrupt the Sveistrup household. Discussions can also become heated, and he tells the story of a female director, new to The Killing, who became very upset at what she perceived to be a ferocious fight between the pair. "And we were like, 'What? We weren't arguing we were just discussing something.'"

Grabol may be close, but there is one thing Sveistrup withholds from her (and from the rest of the cast and crew) until the read-through for the final episode of each series – and that is the identity of the killer. How important is the whodunit element in a TV show that is patently much more than just another murder mystery?

"If you look at Twin Peaks, they laugh at it – they say, 'Let's do the whodunit because it's a cliché.' It really annoyed me that they didn't properly make it mean something. It means something for me – I'm very much a fan of crime stories, especially the good ones."

And one of the many extraordinary things about the first series of The Killing in the UK – given our access to the internet and that it had already been shown all over Europe – was how well kept was the identity of the murderer. No one spilled. For the relatively small but dedicated BBC4 audience, the question of who slayed Nanna Birk Larsen took on the intensity of other such iconic TV mysteries as who killed Laura Palmer, or who shot JR.

Sveistrup describes the success of the first series in the UK as "a rebirth". "It had great reviews all over – in Germany, in Scandinavia – but it wasn't generating any more publicity," he says. "Then, out of the blue, BBC4 took it. I went on holiday to Thailand with my family and I was just checking emails and suddenly there were 15 emails from publishers in England saying, 'Wow, this is good – can we buy the book?' It just exploded. That meant a lot, because your country is not known for reading subtitles."

A country even less known for reading subtitles is America, and Sveistrup's version has never been shown in the US, because it was sold there for a remake. That version has now been axed, but Sveistrup's involvement was minimal. He has, however, been asked to fly over and pitch ideas for new shows. "If they had asked me 10 years ago, I'd probably have run all the way to Los Angeles," he says. "But it's a long way and I have two small kids and a wife, so it would be more realistic for me to work in England if the circumstances were right. I've had a lot of interest from the UK, but I don't think there's been the right project yet.

"I'm a stubborn type and I like working with the actors and with the producer, it's normal for me, but outside Danish Broadcasting, maybe it's old school – the director is king, the writer's more the guy you get some scripts from and then you see him again at the premiere. If they're just looking for a writer, then maybe I'm not the one."

'The Killing III' begins on BBC4 later this month